Gay-Lussac's Law

GAY-LUSSAC'S LAW (Gay-Lus^ac), a quantitative law relating the volume changes of a gas to its temperature, first studied by Lomonosov and then by Gay-Lussac (more accurately called the Lomonosov-Gay-Lussac Law). According to Gay-Lussac's Law, all gases expand equally when heated, and if we call the initial volume of the gas at 0° v₀, and the final volume at temperature t v_t, then at constant pressure, according to Gay-Lussac's Law, we have the following relationship: v_t = v₀ (1 + at)

(1). The constant quantity a is called the coefficient of expansion of gases, and as a first approximation, this quantity is constant for all gases and equal to 1/273. The stated law assumes that the gas pressure is constant. If we change the pressure, keeping the volume of the gas constant, then the initial pressure at 0°, equal to p₀, and the pressure p_t obtained at temperature t are related by the following relationship: p_t = p₀ (1 + at) = p₀ (273 + t)/273

(2). From relationships (1) and (2), it is clear that v_t/v₀ = p_t/p₀ = (273 + t)/273. Thus, the volume of the same gas (at constant p) at temperature t, divided by the pressure (at constant v) at the same temperature, is a constant quantity, independent of temperature. As can be seen from the stated relationship (2), if we take the initial pressure of the gas as the pressure at 0° C, then at 273° C its pressure equals 0. Consequently, the gas at this temperature loses its elasticity. This point is called the absolute zero of gas temperature. Real gases in their expansion differ somewhat from ideal gases, to which Gay-Lussac's Law is strictly applicable. The property of all gases to give the same expansion at different temperatures is used in the construction of thermometers, where the expanding body is a gas, always brought to one volume, and the change in pressure resulting from heating is measured (see Thermometer). Usually in gas thermometers, hydrogen is used as the expanding substance (hydrogen thermometer); for more precise measurements, a helium thermometer is used, which allows investigation of temperatures almost down to absolute zero.